Question

Line AB and BC for a right angle at point B. If A(-3,4) and B(4,4) what is the equation of line BC?

Answer 1

The correct answer is:

x=4.

Step-by-step explanation:

The slope of line AB is given by the formula

`m=(y_2-y_1)/(x_2-x_1)`

Using the coordinates of A and B, we have

`m=(4-4)/(4--3)=(0)/(7)=0`

Perpendicular lines have slopes that are negative reciprocals. Since the slope of AB is 0/7, the reciprocal is 7/0, which is undefined.

Any line with an undefined slope is a vertical line. This will be a vertical line that passes through point B.

Vertical lines have the equation x=c, where c is a constant; since it runs through B, which has coordinates (4, 4), this means the equation is x=4.

Answer 2

Answer: The required equation of line BC is
`x=4.`

Step-by-step explanation: As shown in the attached figure, lines AB and BC meet at right angle at the point B. The co-ordinates of point A and B are (-3, 4) and B(4, 4).

We are to find the equation of line BC.

We know that the slope of a line passing through the points (a, b) and (c, d) is given by

`m=(d-b)/(c-a).`

So, the slope of the line AB will be

`m=(4-4)/(4-(-3))\\\\\Rightarrow m=0.`

Therefore, the equation of the line AB is

`y-4=m(x-4)\\\\\Rightarrow y-4=0\\\\\Rightarrow y=4.`

Since y = constant is the equation of a line parallel to X-axis, so its perpendicular line will be parallel to Y-axis.

So, its equation will be of the form

x = constant.

Since the line BC is perpendicular to AB passing through the point (4, 4), so we must have

`x=4.`

Thus, the required equation of line BC is
`x=4.`